The penalties are another round of legal settlements for the country's biggest bank. In 2013, the bank agreed to pay out $20 billion to end a wide range of lawsuits and investigations relating to past mortgage bond sales and the 2012 "London whale" trade incident.

JP Morgan CEO James Dimon referred to the Madoff case last month at the Goldman Sachs Financial Conference in discussing the strategy behind the settlements.

"You read about Madoff in the paper the other day," Dimon said at the New York conference, the WSJ reported. "We have got to get some of these things behind us so we can do our job. Our job is to serve clients around the world. That's our job. So I want to get it behind us."

The New York Times DealBook wrote that the Madoff deal includes a deferred prosecution agreement. The agreement reportedly states that there would be a suspension of "an indictment as long as JP Morgan acknowledged the facts of the government's case and changed its behavior."

"While no individual executives have been accused of wrongdoing, federal prosecutors are expected to cite JP Morgan for a criminal violation of the Bank Secrecy Act, though prosecutors will only call for a fine and the deferred prosecution agreement, rather than demand the bank plead guilty to the criminal violation as had been considered at one point," wrote DealBook.

DealBook stated that the United States attorney's office in Manhattan, and the FBI, which headed up the case into JP Morgan, declined to comment.